Calculation of the Stresses and Strains in Embedded Fiber Optic Sensors

Abstract

Embedded fiber optic sensors operating on interferometric principles have recently been considered for measuring strains and temperature inside isotropic and orthotropic (composite) materials. Owing to the complex interactions between the sensor and the material surrounding it, the relationship between the sensor output and the strains and temperature inside the material cannot be determined by simple tests. In general, the relationships providing the bridge between the sensor output and the engineering values of strain and temperature must be established via analytical models. Once arrived at, the relationships between the sensor output and the engineering values of the strains and temperature can be inverted to provide the values of the strains and temperature in terms of the sensor output. The scope of this article is limited to the relationship between the strains and temperature in the material, far from the sensor, and the strains and temperature in the sensor. Closed form expressions are derived which relate the strains and temperature in the composite to the strains inside the optical sensor. The sensor may be either circular or elliptic. The sensor and the material surrounding it are considered to be orthotropic.